We have an owned licence for Kayako but don't use it because (last time I checked) there were several problems with the API/API wrapper. What we have now is a really neat integration with Zendesk. We use their cheapest plan but customers interact with us via our own web portal that calls their API (or Xero API for billing, or ServerDensity API for monitoring). The API wrapper for Zendesk is really neat and this works extremely well for very little money.
As we grow and Zendesk starts to get very expensive, we'll likely move to a self-hosted install of Sirportly which I think is about £700 once off including apps and VAT. Apart from the price tag, the main downside with this (in my opinion) is it's RoR. It's a great helpdesk though.
Once upon a time we used Deskpro. That was ok, but the interface is really heavy and the apps are fairly poor. Comes with a nice live chat widget though and it's PHP (based on Symfony).
Not personally a fan of ArcticDesk and I don't think it's been well maintained.